We are given a triangle with one angle measuring $58^\circ$. One of the exterior angles of the triangle measures $103^\circ$. We need to find the measure of angle $f$, which is the interior angle adjacent to the $103^\circ$ exterior angle.

1. Problem Description

We are given a triangle with one angle measuring $58^\circ$. One of the exterior angles of the triangle measures $103^\circ$. We need to find the measure of angle $f$, which is the interior angle adjacent to the $103^\circ$ exterior angle.

2. Solution Steps

Let the unknown interior angle adjacent to the exterior angle of $103^\circ$ be $f$.

We know that the sum of an interior angle and its adjacent exterior angle is $180^\circ$.

Therefore, we have the equation:

$f + 103^\circ = 180^\circ$

Subtracting $103^\circ$ from both sides, we get:

$f = 180^\circ - 103^\circ$

$f = 77^\circ$

3. Final Answer

The size of angle $f$ is $77^\circ$.